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Đáp án+Giải thích các bước giải:

 `c)`

`10x.(x-y)-8.(y-x)`

`=10x.(x-y)+8.(x-y)`

`=(x-y).(10x+8)`

`=2.(x-y).(5x+4)`

`d)`

`(3x+1)^{2}-(x+1)^{2}`

`=(3x+1-x-1).(3x+1+x+1)`

`=2x.(4x+2)`

`=2x.2.(2x+1)`

`=4x.(2x+1)`

`e)`

`x^{3}+y^{3}+z^{3}-3xyz`

`=(x^{3}+3x^{2}y+3xy^{2}+y^{3})+z^{3}-3x^{2}y-3xy^{2}-3xyz`

`=(x+y)^{3}+z^{3}-3xy.(x+y+z)`

`=(x+y+z).[(x+y)^{2}-(x+y).z+z^{2}]-3xy.(x+y+z)`

`=(x+y+z).(x^{2}+2xy+y^{2}-xz-yz+z^{2}-3xy)`

`=(x+y+z).(x^{2}+y^{2}+z^{2}-xy-xz-yz)`

`f)`

`5x^{2}-10xy+5y^{2}-20z^{2}`

`=5.(x^{2}-2xy+y^{2}-4z^{2})`

`=5.[(x^{2}-2.x.y+y^{2})-(2z)^{2}]`

`=5.[(x-y)^{2}-(2z)^{2}]`

`=5.(x-y-2z).(x-y+2z)`

`g)`

`x^{3}-x+3x^{2}y+3xy^{2}+y^{3}-y`

`=(x^{3}+3x^{2}y+3xy^{2}+y^{3})-(x+y)`

`=(x^{3}+3.x^{2}.y+3.x.y^{2}+y^{3})-(x+y)`

`=(x+y)^{3}-(x+y)`

`=(x+y).[(x+y)^{2}-1^{2}]`

`=(x+y).(x+y-1).(x+y+1)`

`h)`

`x^{2}+7x-8`

`=x^{2}-8x+x-8`

`=x.(x-8)+1.(x-8)`

`=(x+1).(x-8)`

`i)`

`x^{2}+4x+3`

`=x^{2}+x+3x+3`

`=x.(x+1)+3.(x+1)`

`=(x+1).(x+3)`

`k)`

`x^{4}+4`

`=x^{4}+4x^{2}+4-4x^{2}`

`=[(x^{2})^{2}+2.x^{2}.2+2^{2}]-(2x)^{2}`

`=(x^{2}+2)^{2}-(2x)^{2}`

`=(x^{2}-2x+2).(x^{2}+2x+2)`

`l)`

`x^{3}-2x^{2}+x-xy^{2}`

`=x.(x^{2}-2x+1-y^{2})`

`=x.[(x^{2}-2.x.1+1^{2})-y^{2}]`

`=x.[(x-1)^{2}-y^{2}]`

`=x.(x-1-y).(x-1+y)`